This page features exercises focused on LU factorizations of various matrices, showcasing the decomposition process into lower and upper triangular forms. It includes solving systems of linear equ...This page features exercises focused on LU factorizations of various matrices, showcasing the decomposition process into lower and upper triangular forms. It includes solving systems of linear equations through LU factorization, detailing intermediate steps and solutions.
Note that xTAx is always a scalar value (e.g., note that xTA=yT for some vector y∈Rn, and yTx is the dot product between x and y and, hence, a real scalar)....Note that xTAx is always a scalar value (e.g., note that xTA=yT for some vector y∈Rn, and yTx is the dot product between x and y and, hence, a real scalar). Exists for every square matrix and says every such matrix, A, is unitarily equivalent to an upper-triangular matrix, T (i.e., there exists an orthonomal basis with respect to which A is upper-triangular)